Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 2x + 2$ and $ JT = 7x - 3$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {2x + 2} = {7x - 3}$ Solve for $x$ $ -5x = -5$ $ x = 1$ Substitute $1$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 2({1}) + 2$ $ JT = 7({1}) - 3$ $ CJ = 2 + 2$ $ JT = 7 - 3$ $ CJ = 4$ $ JT = 4$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {4} + {4}$ $ CT = 8$